Dictionary

morphism en · NOUN

Pronunciation

• /ˈmɔɹfɪzəm/ (General-American)
• /ˈmɔːfɪzəm/ (Received-Pronunciation)
• (US) audio

Etymology

Generalised from isomorphism, etc.

Meanings

1. (formally) An arrow in a category; (less formally) an abstraction that generalises a map from one mathematical object to another and is structure-preserving in a way that depends on the branch of mathematics from which it arises.
   • 1992, Terrance Brown (translator), Gil Henriques, Chapter 13: Morphisms and Transformations in the Construction of Invariants, Terrance Brown (translator), Jean Piaget, Gil Henriques, Edgar Ascher (editors), Morphisms and Categories: Comparing and Transforming, page 198, In certain extreme cases in mathematics, the synthesis of morphisms and of transformations is so intimate that one can speak of a veritable fusion. […] Essentially, categories are sets of morphisms organized into operatory systems.
   • 1982, Israel Program for Scientific Translations (translator), Lev J. Leifman (editor of translation), N. N. Čencov, Statistical Decision Rules and Optimal Inference, American Mathematical Society, Translations of Mathematical Monographs, Volume 53, page 50, 1° The composition of two morphisms is defined if and only if the final object of the first morphism is the initial object of the second. This composition is also a morphism, whose initial object is the initial object of the first morphism and whose final object is the final object of the second.
   • The proof of toroidalization of morphisms of 3-folds to surfaces in [C3] breaks up into two parts: a reduction to prepared morphisms and then a proof of toroidalization of prepared morphisms from n-folds to [surfaces] in [CK]. 2007 November, Steven Dale Cutkosky, “Toroidalization of Dominant Morphisms of 3-Folds”, in Memoirs of the, volume 190, number 890, American Mathematical Society, page 3:
2. Being or having distinct variants of a plant or animal species in the same locale; polymorphism.
   • Briefly, the yellow morphic males can change their status from paired to satellite and from satellite to the paired one. However, they cannot cross into the status of the red morph.[…] The colour morphism of males is proved to be irreversible after its expression at an early stage of ontogeny. 2010, T.J. Pandian, Sexuality in Fishes, page 51:

Forms

Deriveds

zero morphism · apomorphism · monomorphism · comorphism · orthomorphism · diagonal morphism · contactomorphism · homomorphism · catamorphism · morphism set · twist morphism · bimorphism · anamorphism · automorphism · multimorphism · epimorphism · diffeomorphism · constant morphism · classifying morphism · identity morphism · universal morphism · allelomorphism · antimorphism · hylomorphism · isomorphism · homeomorphism · transmorphism · coconstant morphism

Relateds

-morphism · function · bijection · measurable function · functor · isometry

Synonyms

arrow · map

Translations (25)

ja 射 (arrow in a category) · uk морфізм (arrow in a category) · ja 型射 (arrow in a category) · es morfismo (arrow in a category) · de Morphismus (arrow in a category) · ky морфизм (arrow in a category) · pt morfismo (arrow in a category) · ko 사상 (arrow in a category) · cy morffedd (arrow in a category) · fa ریخت (arrow in a category) · fr morphisme (arrow in a category) · fi morfismi (arrow in a category) · is mótun (arrow in a category) · ru морфизм (arrow in a category) · pl morfizm (arrow in a category) · da morfi (arrow in a category) · la morphismus (arrow in a category) · bg морфизъм (arrow in a category) · fi nuoli (arrow in a category) · ba морфизм (arrow in a category) · nl morfisme (arrow in a category) · cs morfismus (arrow in a category) · kk морфизм (arrow in a category) · it morfismo (arrow in a category) · cmn 態射 /态射 (arrow in a category)